Question 8
(IND 5) Show that in the plane there exists a convex polygon of $1992$ sides satisfying the following conditions:
(i) its side lengths are $1,2,3,\ldots,1992$ in some order;
(ii) the polygon is circumscribable about a circle.
Alternative formulation. Does there exist a $1992$-gon with side lengths $1,2,3,\ldots,1992$ circumscribed about a circle? Answer the same question for a $1990$-gon.
(i) its side lengths are $1,2,3,\ldots,1992$ in some order;
(ii) the polygon is circumscribable about a circle.
Alternative formulation. Does there exist a $1992$-gon with side lengths $1,2,3,\ldots,1992$ circumscribed about a circle? Answer the same question for a $1990$-gon.